Submission #567656

#	Time	Username	Problem	Language	Result	Execution time	Memory
567656		toastifishi	Split the sequence (APIO14_sequence)	C++14	100 / 100	399 ms	85320 KiB

sequence

#include <bits/stdc++.h>
#define x first
#define y second
#define all(v) v.begin(), v.end()
using namespace std;

typedef long long ll;
typedef pair<ll, ll> p;

struct CHT{
    ll a[101010], b[101010], c[101010];
    int pv, top;

    void init(){
        pv = top = 0;
    }

    ll f(ll idx, ll x){
        return a[idx]*x + b[idx];
    }

    void insert(ll aa, ll bb, ll cc){
        if(top >= 1 && aa == a[top-1]){
            c[top-1] = cc; return;
        }
        while(top >= 2 && (b[top-1] - b[top-2]) * (a[top-2] - aa) >= (bb - b[top-2]) * (a[top-2] - a[top-1])) top--;
        a[top] = aa;
        b[top] = bb;
        c[top] = cc;
        top++;
        if(pv >= top) pv = top - 1;
    }

    p get(ll x){
        while(pv+1 < top && a[pv+1]*x + b[pv+1] > a[pv]*x + b[pv]) pv++;
        return {f(pv, x), c[pv]};
    }
} cht;

ll arr[101010];
ll sum[101010];
ll dp[2][101010];
int track[222][101010];
vector<int> ans;

int main(){
    ios_base::sync_with_stdio(0); cin.tie(0);
    int n, k; cin >> n >> k;
    for(int i=1; i<=n; i++) cin >> arr[i], sum[i] = sum[i-1] + arr[i];

    for(int i=1; i<=k; i++){
        cht.init();
        cht.insert(0, 0, 0);
        for(int j=1; j<=n; j++){
            auto now = cht.get(sum[j]);
            dp[i&1][j] = now.x;
            track[i][j] = now.y;
            cht.insert(sum[j], dp[i-1&1][j] - sum[j] * sum[j], j);
        }
    }
    cout << dp[k&1][n] << "\n";

    int now = n;
    ans.push_back(-1);
    for(int i=k; i>=1; i--){
        ans.push_back(track[i][now]);
        now = track[i][now];
    }
    sort(all(ans));
    for(int i=1; i<=k; i++){
        if(!ans[i]) ans[i] = 1;
        if(ans[i] <= ans[i-1]) ans[i] = ans[i-1] + 1;
    }
    for(int i=1; i<=k; i++) cout << ans[i] << " ";
    return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:58:36: warning: suggest parentheses around '-' in operand of '&' [-Wparentheses]
   58 |             cht.insert(sum[j], dp[i-1&1][j] - sum[j] * sum[j], j);
      |                                   ~^~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29